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MMLU-Pro / 10538 / We are interested in the capacity of photographic film. The film consists of…

Problem

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question

We are interested in the capacity of photographic film. The film consists of silver iodide crystals, Poisson distributed, with a density of 100 particles per unit area. The film is illuminated without knowledge of the position of the silver iodide particles. It is then developed and the receiver sees only the silver iodide particles that have been illuminated. It is assumed that light incident on a cell exposes the grain if it is there and otherwise results in a blank response. Silver iodide particles that are not illuminated and vacant portions of the film remain blank. We make the following assumptions: We grid the film very finely into cells of area dAdA. It is assumed that there is at most one silver iodide particle per cell and that no silver iodide particle is intersected by the cell boundaries. Thus, the film can be considered to be a large number of parallel binary asymmetric channels with crossover probability 1−100dA1 - 100dA. What is the capacity of a 0.1 unit area film?
Plain-text mathematical notation (without MathML)
We are interested in the capacity of photographic film. The film consists of silver iodide crystals, Poisson distributed, with a density of 100 particles per unit area. The film is illuminated without knowledge of the position of the silver iodide particles. It is then developed and the receiver sees only the silver iodide particles that have been illuminated. It is assumed that light incident on a cell exposes the grain if it is there and otherwise results in a blank response. Silver iodide particles that are not illuminated and vacant portions of the film remain blank. We make the following assumptions: We grid the film very finely into cells of area dA. It is assumed that there is at most one silver iodide particle per cell and that no silver iodide particle is intersected by the cell boundaries. Thus, the film can be considered to be a large number of parallel binary asymmetric channels with crossover probability 1−100dA. What is the capacity of a 0.1 unit area film?
Original LaTeX notation
We are interested in the capacity of photographic film. The film consists of silver iodide crystals, Poisson distributed, with a density of 100 particles per unit area. The film is illuminated without knowledge of the position of the silver iodide particles. It is then developed and the receiver sees only the silver iodide particles that have been illuminated. It is assumed that light incident on a cell exposes the grain if it is there and otherwise results in a blank response. Silver iodide particles that are not illuminated and vacant portions of the film remain blank. We make the following assumptions: We grid the film very finely into cells of area $dA$. It is assumed that there is at most one silver iodide particle per cell and that no silver iodide particle is intersected by the cell boundaries. Thus, the film can be considered to be a large number of parallel binary asymmetric channels with crossover probability $1 - 100dA$. What is the capacity of a 0.1 unit area film?

category

computer science

options

  1. 100.0
  2. 5.0
  3. 0.5
  4. 50.0
  5. 0.1
  6. 2.0
  7. 20.0
  8. 0.01
  9. 1.0
  10. 10.0

src

theoremQA-EECS

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Source and history

upstream_id / Original problem ID
10538
task_id
c067aec5-36dd-52bb-8b48-5b34feb9a0de
task_key
default--test--10538
task_revision_id
1
config / split
default / test

Official source

initial import